离心泵叶轮的参数化设计

对离心泵叶轮优化设计存在的问题进行了详细的阐述,离心泵叶轮优化设计的主要困难在于复杂的内流道形状及其与泵水力性能间复杂的隐式关系,对基于NURBS的曲面设计方法、基于自由曲面变形方法及偏微分方程方法3种离心泵叶轮参数化设计方法的研究进行了详细的介绍．为了减少计算量,采用偏微分方程方法对离心泵叶片几何形状进行参数化控制,参数化控制偏微分方程的边界条件,假定方程中的控制参数a(u,v)为常量1,采用响应面方法对泵叶轮进行优化设计,根据试验及模拟结果进行二阶多项式响应面回归,分析发现二阶多项式响应关系不能反映离心泵叶轮设计目标与控制变量间的复杂的非线性关系．为此,在此基础上提出采用偏微分方程构建设计目标的偏微分超曲面响应,数值求解多维空间上偏微分方程的边值问题,进行优化分析得到最优设计．优化设计实例计算结果表明提出的理论及方法是合理的．

Parametric design of centrifugal pump impellers

The problems in the optimization design of centrifugal pump impeller were elaborated and it was found that the implicit relation between the hydraulic performance and the complicated geometry shape of impeller passages was a main obstacle. The existing parametric design methods for centrifugal pump impellers, such as the NURBS surface method, free surface deformation method and partial differential equation method were introduced in detail. To reduce the computational cost, a partial diffe rential equations method was used to control the geometry shape of centrifugal impellers parametrically, the boundary conditions of the equations were parameterized as well.Suppose the parameters a(u,v) are constant and the response surface methodology (RSM) was applied to optimize the design of centrifugal pump impellers, a 2nd order polynomial response surface was constructed according to the trial results.Unfortunately,  it was identified that a 2nd order polynomial fails to present the complicated nonlinear relation between the objective function and the control variables. So the partial differential equations had to be proposed to construct the hypersurface response of objective function. Then a boundary value problem of hyperspace was numerically solved. Eventually, an optimal design of pump impellers was achieved.The result of the optimized design case shows that the proposed theory and method are reasonable.